How functional dependencies can help full and partial materialization of skycubes



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tarix12.01.2019
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How functional dependencies can help full and partial materialization of skycubes

  • How functional dependencies can help full and partial materialization of skycubes



Discard records with low quality is one dimension of data cleaning

  • Discard records with low quality is one dimension of data cleaning

  • Compare tuples wrt their respective quality parameters

  • Best tuples = those with best tradeoff wrt quality parameters





















Intuitive idea:

  • Intuitive idea:

  • For every A, find the maximal X st X  A

  • Every x  X’s is potentially closed

  • The intersection of these sets of x’s are the closed subspaces





Let X be a subspace.

  • Let X be a subspace.

  • Let Closed={Y | Y is closed}

  • Then, X+ = smallest Y Closed s.t X  Y



















Definition: X Y iff t[X]=t’[X]  t[Y] and t’[Y] incomparable

  • Definition: X Y iff t[X]=t’[X]  t[Y] and t’[Y] incomparable

  • Theorem: Sky(X) satisfies X Y Sky(X)  Sky(XY)

  • Property: XY X Y





Expression = Sky(AB & CD)

  • Expression = Sky(AB & CD)

  • First computes Sky(AB)

  • If t[AB] = t’[AB] and t Sky(AB), then t and t’ are compared wrt C and D





Let  = X1 & … & Xi & … & Xm

  • Let  = X1 & … & Xi & … & Xm

  • If X1…Xi-1  X and X  Xi then

  •  ’ = X1& … & Xi\X & … & Xm

  • AB  C  Sky(AB & CD)  Sky(AB & D)



Functional dependencies are helpful for both full and partial skycube materialization

  • Functional dependencies are helpful for both full and partial skycube materialization

  • Incomparability dependencies characterize skyline inclusions

  • Semantic optimization of prioritized skylines with FDs



Is it possible to come up with a Chase like procedure for priotirized skylines semantic optimization?

  • Is it possible to come up with a Chase like procedure for priotirized skylines semantic optimization?

  • What about Order dependencies ?

  • Incremental maintenance

  • Approximate skylines and approximate FDs

    • t[A] is preferred to s[A] iff s[A] – t[A] > 
    • X  Y iff t, s : t[X] ~ s[X]  t[Y] ~ s[Y]


Thanks

  • Thanks

  • Questions



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